While certain players might opt for wearing cups, plenty of others choose to play baseball roulette with their family jewels. Former third baseman Adrian Beltre, for example, is known for not wearing a cup during games.
Back when I played, a lot of the guys found athletic cups to be very uncomfortable and limiting. I'm sure the designs have gotten better but it was hard to run the bases with a cup rubbing against your thighs. For that reason, a lot of us (even the catcher) decided not to wear them.
It is worth noting, however, that cups are mandatory in some other baseball leagues and organizations. For example, the Cleveland Indians require all players to wear cups, while the Milwaukee Brewers require catchers, infielders, and pitchers to wear them.
The bottom line is, while cups may not be mandatory in the MLB, they are still highly recommended.